Abstract
Abstract
Background
Measures of linkage disequilibrium (LD) play a key role in a wide range of applications from disease association to demographic history estimation. The true population LD cannot be measured directly and instead can only be inferred from genetic samples, which are unavoidably subject to measurement error. Previous studies of r2 (a measure of LD), such as the bias due to finite sample size and its variance, were based on the special case that the true population-wise LD is zero. These results generally do not hold for non-zero $$ {r}_{true}^2 $$rtrue2 values, which are more common in real genetic data.
Results
This work generalises the estimation of r2 to all levels of LD, and for both phased and unphased data. First, we provide new formulae for the effect of finite sample size on the observed r2 values. Second, we find a new empirical formula for the variance of the observed r2, equals to 2E[r2](1 − E[r2])/n, where n is the diploid sample size. Third, we propose a new routine, Constrained ML, a likelihood-based method to directly estimate haplotype frequencies and r2 from diploid genotypes under Hardy-Weinberg Equilibrium. While serving the same purpose as the pre-existing Expectation-Maximisation algorithm, the new routine can have better convergence and is simpler to use. A new likelihood-ratio test is also introduced to test for the absence of a particular haplotype. Extensive simulations are run to support these findings.
Conclusion
Most inferences on LD will benefit from our new findings, from point and interval estimation to hypothesis testing. Genetic analyses utilising r2 information will become more accurate as a result.
Funder
Bill and Melinda Gates Foundation
Publisher
Springer Science and Business Media LLC
Subject
Genetics (clinical),Genetics
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献